小样本量复合肥中氮磷钾高精度预测光谱方法

Objective: N, P, and K, the three main nutrient elements of compound fertilizer products, are essential nutrient elements for crop growth; therefore, the quality inspection of compound fertilizers is very important. Currently, the main methods for detection of compound fertilizer include flame atomic absorption spectrometry, inductively coupled plasma emission spectroscopy (ICP-AES), and near infrared reflectance spectroscopy (NIRS). The detection time of these methods is short. However, samples must be pretreated, thereby preventing real-time monitoring of the samples, and possibly reducing the accuracy of the measurements. Compared with the above technologies, laser-induced breakdown spectroscopy (LIBS) technology requires no sample pretreatment and is characterized by a green and safe detection process, short detection time, and real-time detection of all elements. This technology has been used in various fields. When LIBS technology is combined with partial least squares to model and predict the nutrient elements of compound fertilizers, numerous samples are usually needed to improve the prediction accuracy of the model. The accuracy of prediction is generally low when the sample size is small. Therefore, improving the prediction accuracy for small sample sizes is important. In this article, we propose a data extraction method based on statistical principles to expand sample spectral data for small sample sizes, thereby improving the measurement accuracy. Methods: Twenty types of compound fertilizers, with N, P₂O₅, and K₂O as the main components, were investigated in this work. A LIBS detection system was set up for collecting and analyzing the radiation spectrum of the plasma; then, we used a new proposed method of data extraction. Afterward, the N, P, and K elements in the compound fertilizer samples were modeled and predicted using a partial least square method combined with principal component analysis. The last 75 sets of spectra were used as T2 spectra to obtain the relative error between the true N, P, and K element content of each sample and the predicted content. To determine the robustness of the calibration model, we randomly removed five samples for modeling and predicting the N, P, and K content of these samples. Results and Discussions: The spectral data were preprocessed. Compared with the original spectrum, the background of the preprocessed spectrum is eliminated, and the relative intensity between channels changes, but the relative intensity of each spectral line between the channels remains unchanged (Fig. 3). The N, P, and K elements are modeled and predicted after the preprocessing steps. The coefficients of determination for N, P, and K element content modeling in the training set are 0.99, 0.98, and 0.99, respectively, and the root mean square errors are 0.4309, 0.0979, and 0.3385, respectively; moreover, the coefficients of determination obtained for the fitting curves of the predicted and true values of the N, P, and K element contents in the prediction set are 0.99, 0.98, and 0.99, respectively, and the root mean square errors are 0.4787, 0.0706, and 0.0195, respectively (Fig. 5, Fig. 7, and Fig. 9). The average relative errors between the true and predicted values of the N, P, and K element contents of 20 samples obtained from T2 spectra are 2.33%, 0.70%, and 3%, respectively (Fig. 6, Fig. 8, and Fig. 10). After the sample data are expanded, the average predicted relative error (ARE) values of N, P, and K elements in the 20 compound fertilizer samples are all <3%, and ARE of P is <1%. Compared with the unexpanded condition, the average relative error of the measured element content dropped by more than 10% (Table 2). The robustness of the model is determined. The predicted values of N and P content agree well with the true values, the relative errors are all below 12%, and the relative errors of K element are mostly above 20% (Table 3, Table 4, and Table 5). Conclusions: In this work, the partial least square quantitative analysis method is used to establish a regression model, and a data extraction method based on statistical principles is used to expand the small sample size of the compound fertilizer spectral data. The N, P, and K element content of a compound fertilizer sample is modeled and predicted. The average relative errors of the content prediction in 20 samples are 2.33%, 0.70%, and 3.00%, respectively. Further, the robustness of the model is determined by randomly removing the data of five samples. The results reveal that the predicted values of N and P element content concur with the actual values, and the relative errors are mainly below 12%. Thus, after using the data extraction method based on statistical principles to expand the sample spectrum data, the average relative error of the measured element content is reduced by more than 10% compared with the unexpanded time. The experimental results show that when the sample size is small, the accuracy of the measurement can be improved using this new data extraction method combined with the partial least square quantitative analysis model for regression modeling.